The edge connectivity augmentation problem is closely related to edge splitting off, a widely used tool in the graph connectivity literature (e.g., [1]}, [2]}). A pair of (weighted) edges \((u, s)\)  and \((s, v)\)  both incident on a common vertex \(s\)  is said to be split off by weight \(w\)  if we reduce the weight of both these edges by \(w\)  and increase the weight of their shortcut edge \((u, v)\)  by \(w\) . Such a splitting off is valid if it does not change the (Steiner) connectivity of the vertices \(V\setminus \lbrace s\rbrace \) . If all edges incident on \(s\)  are eliminated by a sequence of splitting off operations, we say that the vertex \(s\)  is split off. We call the problem of finding a set of edges to split off a given vertex \(s\)  the edge splitting off problem.
